The term “cyclic prefix” is used in the communications field to refer to the affixing of a tail section of a signal at the beginning of the original signal, to create a slightly lengthened signal. This technique is often used in communication systems to emulate the circular convolution of a transmitted signal with the time-invariant impulse response of the communication channel, since the periodic nature of circular convolution provides many advantages in discrete signal processing. Cyclic-prefix techniques are applied, for example, in wireless communication systems using Orthogonal Frequency Division Multiplexing (OFDM), such as in the Long-Term Evolution (LTE) wireless systems developed by members of the 3rd-Generation Partnership Project (3GPP). Cyclic prefixes are also used in the design of signature sequences, which are widely used in communication systems for the purposes of synchronization, signal identification, and the like.
In OFDM systems, the use of cyclic prefixes “attached” to the beginning of each transmitted OFDM symbol allows the receiver to treat the received symbol as though it were a circular convolution of the transmitted symbol with the communication channel response. As a result, the receiver can use a simple Discrete Fourier Transform (DFT) to demodulate the received signal. In signature sequence design applications, the use of a cyclic prefix allows a “root signal” to be subjected to different circular time shifts and frequency shift, to create multiple signature sequences from the same root sequence. If the root sequence is properly chosen, these multiple versions can be used to identify multiple devices or signal sources.
In the standardization of Long-Term Evolution (LTE) wireless communications technology there have been efforts to design signature sequences to be used for mobile positioning. The sequences for this application need to occupy a time slot in which some segments are already occupied by the transmission of existing Cell-specific Reference Symbols (CRS). Accordingly, it is desirable to keep the new sequences to be used for positioning orthogonal to the existing CRS in time. Thus, any new sequence that is designed for positioning applications will likely not be transmitted as a single continuous signal, due to the presence in each slot of OFDM symbols carrying the existing CRS. Since the signature sequence will comprise non-contiguous segments, conventional approaches such as those based on the cyclic-prefix Zadoff-Chu sequence set are no longer applicable. Instead, some form of frequency hopping pattern is likely to be used, potentially leading to degraded performance due to the non-ideal auto-correlation characteristics of the sequence.
When a frequency-hopping pattern is used for a signature sequence, the auto-correlation properties that determine the performance of the signature sequence are generally not as good as those for other time-domain-based sequences, such as the m-sequence or the Zadoff-Chu sequence. This is due largely to the limitations of the signal structure, which allows only one of a finite number of sinusoids to be transmitted in a given interval.
It has been shown that a large set of sequences with ideal circular auto- and cross-correlation functions can be derived from a properly chosen root sequence by introducing unique cyclic time-frequency shifts. These unique sequences can be used for identification and synchronization purposes, and generally have better properties than frequency-hopping sequences. However, these sequences cannot be used in non-contiguous transmission situations.